Sixty percent of college-bound high school graduates aren’t prepared for college success, according to ACT’s Condition of College & Career Readiness 2012 report. Fifty-two percent of graduating seniors took the ACT exam, which claims to measure both college and career readiness: Only 25 percent met the benchmarks in all four subject areas, English, reading, math and science. Twenty-eight percent did not meet any benchmark; another 15 percent met only one and 17 percent met just two.

A student who meets the benchmark has a 75 percent chance of earning a C or higher in that subject area in a first-year college class and a 50 percent chance of earning a B. The benchmarks are based on the college grades earned by ACT-tested students.

Test takers are improving in mathematics and science, while English and reading scores have been flat for several years.

Forty-six percent of ACT-tested graduates are prepared in math, 31 percent in science, 67 percent in English and 52 percent in reading.

The sample test questions in writing, reading and math were very easy. The science question required reading and logic skills, but no actual knowledge of science.

What grade level is this math question?

Near a large city, planes take off from two airfields. One of the fields is capable of sending up a plane every 3 minutes. The other field is capable of sending up 2 planes every 7 minutes. At these rates, which of the following is the most reasonable estimate of the total number of planes the two airfields could send up in 90 minutes?

A. 18

B. 27

C. 36

D. 44

E. 55

A majority of ACT-taking 12th graders can’t solve questions like this? Some states are requiring all graduating seniors to take the ACT, regardless of their college plans, so there are more marginal students taking the exam. But still.

For my money, that’s about a 6th grade math question, but I haven’t been around K-12 math in person for a long, long time. The problem does not, after all, require real algebra or any other higher math, just arithmetic and reasoning about things. Doesn’t that make it a pre-algebra question?

Not only were the sample questions pretty easy (the one about Huey Long required some pretty fine judgement, though, and I think you could justify more than one answer if you tried hard), the Chemistry question wasn’t so much about chemistry as materials science.

If these questions are truly indicative of the test difficulty and if only 40% of our high school graduates (college bound or not) can answer them, then things are even worse than I thought.

And most of these kids have taken and *passed* algebra.

The answer is 55 (approximately)…

1 plane every 3 minutes = 30 planes in 90 mins

2 planes every 7 minutes is approximately 24 planes in 88 minutes

which works out to 54 planes total.

If a majority of the students who took the ACT couldn’t handle this question (which at best is perhaps middle school math) or perhaps very basic algebra, one wonders what the students math grades were (probably inflated beyond all imagination here).

This problem didn’t take much effort to solve, but rather the ability to analyze and think out the problem while doing it.

Of course, students have HATED word problems since day one

Rate problems are always difficult to learn.

And it is easy to forget how to do them if you don’t (a) REALLY learn them [instead of just for the test], or (b) actually need to solve them for a while.

I could argue the best estimate is C-44, since 55 is not possible given the information. The questions says what is the best reasonable estimate, and I can see where students wouldn’t pick D bc it is not possible.

Why is it not possible? Are you reading “capable of sending up 2 planes every 7 minutes” as meaning that planes at that field always take off in pairs, and thus the answer has to be an even number?

The question is poorly posed, because we don’t know what to do about the boundry conditions. If we started at airport open, in the 2nd 90 minute block, we’d get 56 planes. From the first 90 minute block we’d get only 54 planes. 55 is a decent answer for the longer period as it averages the two. But, we don’t know WHERE we are in the day, so it’s not obvious. Playing the “Price is Right” card seriously underestimates capacity.

54 would have been a nice choice to give the kids though; since 55 isn’t possible without reading in a bit.

The key word in the question is “estimate.” 55 is a little higher than the reasonable exact answer, but it’s much closer than 44.

Of course, if you solve it as a simple proportion, you get 55.71 ish. So maybe that’s what the test makers expected the kiddos to do – we’re all overanalyzing.

Plus, if you know anything at all about planes, you know that they don’t take off in increments measured to the second. Thus the rates given in the problem are obviously average expected rates, not precise-down-to-the-second rates that would actually be achieved. And anyway the question asks explicitly for an “estimate.”

I think it is perfectly clear that 55 is the best answer. 44 would not be a good answer for any purpose under any reading of the question. I don’t know what Mike in Texas is thinking, but it worries me a little that he’s a science teacher.

Ed,

I’m trying to think of it as how a child may see it and there are several ways to interpret the question.

First, if you take it strictly by the numbers I can easily see students deciding the answer 55 is not a reasonable estimate b/c it is impossible. The maximum amount would be 54.

HOWEVER, if you happen to live close enough to an airport and watch the traffic pattern you would probably decide, that since 90 divided by 7is 12 with 6 left over, and given that 3minutes 30 seconds is half of 7, it would take 87 minutes and 30 seconds to launch 25 planes from the 2nd airport, and therefore the correct answer is exactly 55.

Where I teach very few children would have the experience to choose the 2nd option, having never been near a major airport and having a local airport that probably only averages 1 takeoff or landing an hour.

This is a poorly constructed question. An easy fix would be to ask how many airplanes would take off from the two airports in 90 minutes, leaving 55 to be the correct answer, keeping it purely mathematical and eliminating the influence of the prior experience of either having or not having been to a major airport. You could also change the answer choices to something very close, but not over, 55 and fix it also.

I REALLY hope Mike in Texas does not teach math. You keep saying 55 is “impossible.” The problem clearly said “estimate.” If you ignore the fact the number of planes must be a whole number and treat it as a “rate addition” problem, then the exact number of planes would be around 55.14, which rounds to 55. I don’t think the test-writers expected students to solve it that way, but instead solve it via estimation. The problem is perfectly worded and well-posed, and there is absolutely NO ambiguity in what is going on.

(And before you rage at me, I am a liberal Democrat who supports teachers and unions.)

That question doesn’t require analysis, just a quick eyeballing and estimate. 1 plane every 3 minutes is 30 in 90 minutes; 2 planes per 7 minutes is slightly less, so the number is going to be a bit under 60. 44 is obviously far too low, so the answer has to be 55.

That question is probably used to test the “math skill” of estimation which is part of the modern curriculum. (In a sane world we’d train kids to calculate precisely, and let them estimate on their own once they have the analytical skills cold and can use them without thinking.)

In a sane world we’d train kids to calculate precisely, and let them estimate on their own once they have the analytical skills cold and can use them without thinkingYes.

In my opinion, this question doesn’t teach estimation. It essentially requires a student to solve for the exact answer, then choose the option closest to the exact answer. That isn’t estimation.

One could approach the problem in another way. 1 plane per three minutes is very close to 2 planes per 7 minutes. Thus, every 7 minutes about 4 planes take off. 91/7 = 13. 13 x 4 = 52. You know the answer’s a little larger, because you know you fudged the number of planes to the low side in the first step.

However, it isn’t an estimation. It’s hard to teach estimation to beginning math students.

I don’t know what you think estimation is. The minute you use the word “fudge”, you’re there.

The first airport is sending out 30 planes.

So initial question to ask is whether the second airport is sending out more or fewer than the first. So doubling the ratio, the airport would send out 2 planes in 6 minutes, not 7. So the answer must be less than 60 (which is obvious from looking at the answers, too).

At that point, it’s also pretty obvious that the answer is close to 60, so 55 is a logical guess. But to be complete, the next question would be “more or less than half”? that is, is the second airport sending out more than half as many, or less than half as many? This is, again, the obvious delineator because half of 30 is 45, and the next largest number is 44, which should reaffirm to the student that he or she is on the right track.

And again, it should be obvious that the rate will send off more than half again as many planes, making 55 the obvious answer. But if it’s not certain, then you double the time it takes the first airport to send out planes, which would be 1 plane every 6 minutes–obviously fewer than the second airport.

Most test prep instructors cover this method. Math teachers don’t, as a rule. (I do, but that’s because I began my teaching life as a test prep instructor).

Yes, the method I just proposed is an estimation, but it’s more effort to create the estimate than to solve the problem exactly. I don’t think the test taker would gain any time by using the method I proposed for this problem–as long as said test taker has mastered arithmetic.

Now, if the problem had added an extra step, one might reach a point at which it was worthwhile to estimate. Change the planes leaving to planes arriving. Then, add “each plane requires between 100 and 200 liters of fuel to take off again. What is the best estimate of the minimum supply of fuel the airport should have on hand to guarantee all the planes arriving in a 90 minute interval can leave the airport again? ” Give answers such as:

A. 850 liters

B. 5500 liters

C. 11000 liters

D. 25000 liters

The ACT is not an easy test. Its math, in particular, is more difficult than SAT math. Second, the single most difficult aspect of the ACT is its timing, which makes its College Readiness report complete crap. I love the test, but this report is fraud.

In the math section,it often throws in relatively easy but word heavy problems–even more commonly in the last 10 questions of the test. Students take the test under extreme time pressure. Very commonly, the ones they’ll skip will be the wordy ones, unless they’ve been coached to know that they are easier than they look. Even more commonly, they won’t even get to the last 10 questions.

Without knowing where the question appeared in the test, you can’t know anything about how many students actually worked it and missed it, as opposed to skipped it because of time concerns (due to length) or never got there.

‘

This looks like the kind of homework problem my son came home with last year… in 3rd grade! He was *supposed* to solve the problems by estimating, because he hadn’t learned enough math yet to do anything else (they were just beginning division). Did I learn to hate his math homework? Yes I did… Hooray for Cupertino schools, maybe.

Even in Cupertino, no, your kids were NOT doing this in 3rd grade. Although the level of math in this problem is low (division), the abstract thinking necessary to do a multi-step word problem is not something normal 3rd graders can grasp. No doubt some really exceptional 3rd graders could handle this, but not a mixed-ability public school classroom.

I didn’t say my kid could *do* the problems of that type – he sat and cried and I sent the homework back in unfinished. But yes, we did get problems like that (occasionally, not constantly).

Russian 3rd graders (maybe second graders) get multi-step word problems. It is one of the more interesting things about Russian elementary school mathematics (along with the tractor problems).

I have grades 1-3 in translation of a/the Russian mathematics textbook series and I checked.

I don’t know what Cupertino does, but this assignment doesn’t seem implausible.

Uhm … because only 30% of Americans should go to college anyway? Yeah, that’s about right.

Jab,

You will note I said I was trying to think of ways students would interpret the question.

Like everyone else here I know the correct answer is 55, but I’ve also seen kids make very different interpretations of questions.

Also, Ed made the statement “Plus, if you know anything at all about planes, you know that they don’t take off in increments measured to the second.” This assumes students have knowledge of planes and the traffic patterns around airports. While that may be true of students in Houston it is not true in my neck of the woods. I suggested ways to make the question better.

I wholeheartedly agree with Engineer-Poet when he says lets train the kids to calculate precisely and worry about estimation later.

During the Iowahawk takedown of the comparison of TX vx WI in ed results, the guy also explained quite clearly that the SAT scores are inversely proportional to the number of kids taking the test. IIRC, in Maine all HS kids take the SAT and the scores are low.

If more and more kids are taking the ACT, it would seem reasonable that some of them are from the cohort which would not have done so in the past due to lack of interest in, or confidence in, or plans for future education. IOW, a lower-achieving bloc.

Another thing to control for.

Unless we’re sending the bottom 5% of high school graduates to take the ACT, this just doesn’t look like a high school math problem to me.